代数几何研讨班:On the positivity of high-degree Schur classes of an ample vector bundle

中科院数学与系统科学研究院

数学研究所

代数几何研讨班

报告人：肖 建 （清华大学）

题  目：On the positivity of high-degree Schur classes of an ample vector bundle

时  间：2020.12.09（星期三），15:00-16:00

地  点：晨兴 510室

摘  要：Let X be a smooth projective variety of dimension n, and let E be an ample vector bundle over X. We show that any non-zero Schur class of E, lying in the cohomology group of bidegree (n-1, n-1), has a representative which is strictly positive in the sense of smooth forms. This conforms the prediction of Griffiths conjecture on the positive polynomials of Chern classes/forms of an ample vector bundle on the form level, and thus strengthens the celebrated positivity results of Fulton-Lazarsfeld for certain degrees.